[latex]d) \log_{frac15}3*log_37*log_7625= \frac{log_53}{log_5frac15}*frac{log_57}{log_53}*frac{log_5625}{log_57}= \-log_55^4=-4 \... \log_ab=frac{log_cb}{log_ca}[/latex] Przyklady b) i c) w zalaczniku
Prawa działąń na logarytmach: [latex]log_a{(b_{1}*b_{2})}=log_a{b_{1}}+log_a{b_{2}}\ log_a{frac{b_{1}}{b_{2}}}=log_a{b_{1}}-log_a{b_{2}}\ log_a{b^{n}}=n*log_a{b}\ log_a{b}=frac{log_c{b}}{log_c{a}}\ log_a{b}=frac{1}{log_b{a}}[/latex] Własność logarytmu: [latex]log_a{a}=1[/latex] ========================================= b) [latex]frac{1}{2}log_5{4}*log_2{30}-log_5{6}=frac{1}{2}log_5{2^{2}}*log_2{30}-log_5{6}=\ =frac{1}{2}*2frac{1}{log_2{5}}*log_2{30}-log_5{6}=frac{log_2{30}}{log_2{5}}-log_5{6}=\ =log_5{30}-log_5{6}=log_5{(30:6)}=log_5{5}=1[/latex] ----------------------------------------------------- c) [latex]log_4{9}*log_3{128}=log_4{3^{2}}*log_3{2^{7}}=2frac{1}{log_3{2^{2}}}*7log_3{2}=\ =frac{14}{2}*frac{log_32}{log_3{2}}=7log_2{2}=7*1=7[/latex] ----------------------------------------------------- d) [latex]log_frac{1}{5}{3}*log_3{7}*log_7{625}=frac{1}{log_3{5^{-1}}}*log_3{7}*log_7{5^{4}}=\ =-frac{log_3{7}}{log_3{5}}*4frac{1}{log_5{7}}=-4log_5{7}*frac{1}{log_5{7}}=-4frac{log_5{7}}{log_5{7}}=\ =-4*log_7{7}=-4[/latex]
